How to stop texture curving around a hole?
You could select upward faces, go in top view and hit U, Project From View (bounds) to fit the faces to your map, but then the other faces wouldn't be unwrapped, so you'd have to unwrap then separately.

If you're going to export it to Unity, you might as well triangulate the mesh inside Blender with CTRL + T before unwrapping, it may work better without NGons.